12.The spot is 10, if you think one-month later, the price will be 8 and 10 with equal probability, risk-free interest rate is 5%, what is the price of call option strike at 10? (between 5/1.05 and 10/1.05 because of risk-free probability.)

13.Gaussian copula: hazard rate of A and B are 1% and 2%. A contract pay you $1 if A defaults earlier than B. The price of the contract has lowest price when the correlation is (0, 75%, 100%, ...)?

14.Monte Carlo: to find out the mean of A, find a variable B, corr(A,B)=c, and simulate A + B(E(B)-B) instead of A. What is B? ( cov(a,b)/var(a), cov(a,b)/var(b), 1, -1 )

15.Monte Carlo: need to simulate some rare event, so u need to simulate in a different measure. What is the name of this technique? (sequential resampling?)

16.Variance of \int(t1,t2) of Wt^2dWt, and some other ito’s integral problems

17.Dividend-paying stock (discrete dividend), the price difference of modeling in GBM and jump-diffusion

Finance (FI and options)

1. Bond: 5% coupon, (10year?) 1000 face, 6% yield, price?

2. Bond: 3% coupon 10 year bond traded at par(100), what is the price if rate goes up 1bp: (99.91, 99.99, 100.01, ...)

3. Which is higher? FRA vs. Eurodollar futures

4. At 2009, a trader believes that dividend in 2011 is lower than expectation, strategy? long/short 2010 forward and long/short 2011 forward?

8. Long long-term ATM call and short short-term ATM call, adjust the ratio to make total vega zero. If before expiry of the short-term option, spot = strike again, vega: positive, negative, zero? (positive?)

9.The trader wants to do a delta-hedge strategy, but he plugs wrong sigma1>implied vol, assume the portfolio is -C+delta*S, what will the portfolio value change? when the stock increase/decrease, the value increase/decrease..

2. static member initialization: simple case (choose the one initialized out of the class)

3. static member initialization: In template class, how many instances? 1) Cannot have static member in template class 2) only one instance 3) as many as instances of classes 4) as many as instantiations of classes